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2_finite_elements.html

@@ -72,7 +72,7 @@
 <div class="proof proof-type-definition" id="id5">
 <span id="def-ciarlet"></span>
     <div class="proof-title">
-        <span class="proof-type">Definition 2.44</span>
+        <span class="proof-type">Definition 2.43</span>
 
     </div><div class="proof-content">
 <p>A <em>finite element</em> is a triple <span class="math notranslate nohighlight">\((K, P, N)\)</span> in which <span class="math notranslate nohighlight">\(K\)</span> is a cell,
@@ -85,7 +85,7 @@
 <div class="proof proof-type-definition" id="id6">
 <span id="nodalbasis"></span>
     <div class="proof-title">
-        <span class="proof-type">Definition 2.45</span>
+        <span class="proof-type">Definition 2.44</span>
 
     </div><div class="proof-content">
 <p>Let <span class="math notranslate nohighlight">\(N = \{\phi^*_j\}\)</span> be a basis for <span class="math notranslate nohighlight">\(P^*\)</span>.  A <em>nodal
@@ -239,7 +239,7 @@ <h2><span class="section-number">2.3. </span>The Lagrange element nodes<a class=
 <div class="proof proof-type-exercise" id="id7">
 <span id="ex-lagrange-points"></span>
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.46</span>
+        <span class="proof-type">Exercise 2.45</span>
 
     </div><div class="proof-content">
 <p>Use <a class="reference internal" href="#equation-lattice">(2.6)</a> to implement
@@ -307,7 +307,7 @@ <h2><span class="section-number">2.3. </span>The Lagrange element nodes<a class=
 <div class="proof proof-type-exercise" id="id8">
 <span id="ex-vandermonde"></span>
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.47</span>
+        <span class="proof-type">Exercise 2.46</span>
 
     </div><div class="proof-content">
 <p>Use <a class="reference internal" href="#equation-vandermonde">(2.7)</a> to implement
@@ -349,7 +349,7 @@ <h2><span class="section-number">2.5. </span>Implementing finite elements in Pyt
 <div class="proof proof-type-exercise" id="id9">
 <span id="ex-finite-element"></span>
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.48</span>
+        <span class="proof-type">Exercise 2.47</span>
 
     </div><div class="proof-content">
 <p>Implement the rest of the
@@ -390,7 +390,7 @@ <h2><span class="section-number">2.6. </span>Implementing the Lagrange Elements<
 <div class="proof proof-type-exercise" id="id10">
 <span id="ex-lagrange-element"></span>
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.49</span>
+        <span class="proof-type">Exercise 2.48</span>
 
     </div><div class="proof-content">
 <p>Implement the <code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code> method of
@@ -438,7 +438,7 @@ <h2><span class="section-number">2.7. </span>Tabulating basis functions<a class=
 <div class="proof proof-type-exercise" id="id11">
 <span id="ex-tabulate"></span>
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.50</span>
+        <span class="proof-type">Exercise 2.49</span>
 
     </div><div class="proof-content">
 <p>Implement <a class="reference internal" href="fe_utils.html#fe_utils.finite_elements.FiniteElement.tabulate" title="fe_utils.finite_elements.FiniteElement.tabulate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">tabulate()</span></code></a>.
@@ -489,7 +489,7 @@ <h2><span class="section-number">2.8. </span>Gradients of basis functions<a clas
 <div class="proof proof-type-exercise" id="id12">
 
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.51</span>
+        <span class="proof-type">Exercise 2.50</span>
 
     </div><div class="proof-content">
 <p>Extend <a class="reference internal" href="fe_utils.html#fe_utils.finite_elements.vandermonde_matrix" title="fe_utils.finite_elements.vandermonde_matrix"><code class="xref py py-meth docutils literal notranslate"><span class="pre">vandermonde_matrix()</span></code></a> so that
@@ -520,7 +520,7 @@ <h2><span class="section-number">2.8. </span>Gradients of basis functions<a clas
 <div class="proof proof-type-exercise" id="id13">
 
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.52</span>
+        <span class="proof-type">Exercise 2.51</span>
 
     </div><div class="proof-content">
 <p>Extend <a class="reference internal" href="fe_utils.html#fe_utils.finite_elements.FiniteElement.tabulate" title="fe_utils.finite_elements.FiniteElement.tabulate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">tabulate()</span></code></a> to
@@ -591,7 +591,7 @@ <h2><span class="section-number">2.9. </span>Interpolating functions to the fini
 <div class="proof proof-type-exercise" id="id14">
 <span id="ex-interpolate"></span>
     <div class="proof-title">
-        <span class="proof-type">Exercise 2.53</span>
+        <span class="proof-type">Exercise 2.52</span>
 
     </div><div class="proof-content">
 <p>Implement <a class="reference internal" href="fe_utils.html#fe_utils.finite_elements.FiniteElement.interpolate" title="fe_utils.finite_elements.FiniteElement.interpolate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">interpolate()</span></code></a>.</p>

6_finite_element_problems.html

@@ -317,13 +317,13 @@ <h3><span class="section-number">6.2.4. </span>Sparse matrices<a class="headerli
 are avoided.</p>
 <div class="admonition hint">
 <p class="admonition-title">Hint</p>
-<p>The <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.html#module-scipy.sparse" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse</span></code></a> package provides convenient interfaces
+<p>The <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.html#module-scipy.sparse" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse</span></code></a> package provides convenient interfaces
 which enable Python code to employ a variety of sparse matrix
 formats using essentially identical operations to the dense matrix
 case. The skeleton code already contains commands to construct
 empty sparse matrices and to solve the resulting linear system. You
 may, if you wish, experiment with choosing other sparse formats
-from <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.html#module-scipy.sparse" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse</span></code></a>, but it is very strongly suggested that
+from <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.html#module-scipy.sparse" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse</span></code></a>, but it is very strongly suggested that
 you do <strong>not</strong> switch to a dense numpy array; unless, that is, you
 particularly enjoy running out of memory on your computer!</p>
 </div>

9_mixed_problems.html

@@ -174,7 +174,7 @@ <h3><span class="section-number">9.1.2. </span>Tabulation<a class="headerlink" h
 <h3><span class="section-number">9.1.3. </span>Nodes<a class="headerlink" href="#nodes" title="Permalink to this headline">¶</a></h3>
 <p>Even though we didn’t need the nodes of the <code class="xref py py-class docutils literal notranslate"><span class="pre">VectorFiniteElement</span></code> to
 construct its basis, we will need them to implement interpolation. In
-<a class="reference internal" href="2_finite_elements.html#nodalbasis"><span class="std std-numref">Definition 2.45</span></a> we learned that
+<a class="reference internal" href="2_finite_elements.html#nodalbasis"><span class="std std-numref">Definition 2.44</span></a> we learned that
 the nodes of a finite element are related to the corresponding nodal basis by:</p>
 <div class="math notranslate nohighlight" id="equation-9-mixed-problems-3">
 <span class="eqno">(9.6)<a class="headerlink" href="#equation-9-mixed-problems-3" title="Permalink to this equation">¶</a></span>\[\mathbf{\Phi}^*_i(\mathbf{\Phi}_j) = \delta_{ij}\]</div>
@@ -380,7 +380,7 @@ <h3><span class="section-number">9.4.1. </span>Assembling block systems<a class=
 </div>
 <p>This means that one can first create a full vector of length <span class="math notranslate nohighlight">\(n+m\)</span> and then
 slice it to create subvectors that can be used for assembly.</p>
-<p>Conversely, <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.html#module-scipy.sparse" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse</span></code></a> provides the <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.bmat.html#scipy.sparse.bmat" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-func docutils literal notranslate"><span class="pre">bmat()</span></code></a>
+<p>Conversely, <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.html#module-scipy.sparse" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse</span></code></a> provides the <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.bmat.html#scipy.sparse.bmat" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-func docutils literal notranslate"><span class="pre">bmat()</span></code></a>
 function which will stitch together a larger sparse matrix from blocks. In
 order to have the full indexing options you are likely to want for imposing the
 boundary conditions, you will probably want to specify that the resulting
@@ -408,15 +408,15 @@ <h3><span class="section-number">9.4.3. </span>Solving the matrix system<a class
 <p>The block matrix system that you eventually produce will be larger than many of
 those we have previously encountered, and will have non-zero entries further
 from the diagonal. This can cause the matrix solver to become expensive in both
-time and memory. Fortunately, <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.linalg.html#module-scipy.sparse.linalg" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse.linalg</span></code></a> now incorporates an
+time and memory. Fortunately, <a class="reference external" href="http://scipy.github.io/devdocs/reference/sparse.linalg.html#module-scipy.sparse.linalg" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse.linalg</span></code></a> now incorporates an
 interface to <a class="reference external" href="https://portal.nersc.gov/project/sparse/superlu/">SuperLU</a>,
 which is a high-performance direct sparse solver. The recommended solution
 strategy is therefore:</p>
 <ol class="arabic simple">
-<li><p>Convert your block matrix to <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.csc_matrix.html#scipy.sparse.csc_matrix" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy.sparse.csc_matrix</span></code></a>, which is the
+<li><p>Convert your block matrix to <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.csc_matrix.html#scipy.sparse.csc_matrix" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy.sparse.csc_matrix</span></code></a>, which is the
 format that SuperLU requires.</p></li>
-<li><p>Factorise the matrix using <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.linalg.splu.html#scipy.sparse.linalg.splu" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.sparse.linalg.splu()</span></code></a>.</p></li>
-<li><p>Use the resulting <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.linalg.SuperLU.html#scipy.sparse.linalg.SuperLU" title="(in SciPy v1.11.0.dev0+1388.e6c27e5)"><code class="xref py py-class docutils literal notranslate"><span class="pre">SuperLU</span></code></a> object to finally solve
+<li><p>Factorise the matrix using <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.linalg.splu.html#scipy.sparse.linalg.splu" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.sparse.linalg.splu()</span></code></a>.</p></li>
+<li><p>Use the resulting <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.sparse.linalg.SuperLU.html#scipy.sparse.linalg.SuperLU" title="(in SciPy v1.11.0.dev0+1409.6d43301)"><code class="xref py py-class docutils literal notranslate"><span class="pre">SuperLU</span></code></a> object to finally solve
 the system.</p></li>
 </ol>
 </section>